What is an aspect ratio?
Every photo or movie has an attribute called an Aspect Ratio. The aspect ratio is the relation between the horizontal and vertical sizes of the photo. To calculate the aspect ratio simple divide the width or a photo by its height. For example TV in normal mode has an aspect ratio of 4:3 or in other words if we were to divide the width of the screen by its height the result would be 4/3. TV in widescreen format on the other hand has an aspect ratio of 16:9.
When we take a photo with a camera light that travels through the lenses hits a sensor (a film in traditional cameras or a CCD in digital ones). The sensor in turn translates the light into a two dimensional photo. The sensor itself has physical attributes such as width, height, granularity (in films) and number of pixels (in digital CCD sensors).
The connection between an aspect ratio and photo printing
When photos are printed on paper the aspect ratio of the paper must be the same as the aspect ratio of the sensor that was used to take the photo. If the aspect ratios are different the result will be a blank area left on the paper or a stretched photo that fits the paper but distorts the objects in it.
Why does it happen? The answer is pretty simple. For the sake of explanation lets assume a photo sensor that is 6 inches wide and 4 inches high (real sensors are much smaller). Lets assume that we are trying to print the a photo taken with that sensor on a paper that is 4 inches high. If the paper width would be less than 6 inches we will have to crop part of the photo since there wont be enough space available on the paper. If the paper width is more than 6 inches we will have to leave a blank area on the paper since we do not have enough photo to print on more than 6 inches. If we want our photo to exactly fit the page we can stretch or shrink the photo horizontally to whatever the paper size is but then the objects in the print will be distorted and look more fat or thin as they were in real life.
Printing on a 4X6 paper
One of the most common paper sizes is 4X6. This size was used for many years for printing photos taken with traditional film cameras. The traditional film had an aspect ratio of 3:2 and thus the photos taken with a traditional film camera would fit perfectly on a 4X6 papers.
For reasons beyond the scope of this article digital cameras use sensors with a different aspect ratio than tradition film cameras. The following table summarizes popular image sizes in pixels and the respective aspect ratio (sensor pixels, width X height and aspect ratio):

2 MP 1600 X 1200 aspect ratio 4:3
3 MP 2048 X 1536 aspect ratio 4:3
4 MP 2272 X 1704 aspect ratio 4:3
5 MP 2592 X 1944 aspect ratio 4:3
6 MP 2816 X 2112 aspect ratio 4:3
8 MP 3200 X 2400 aspect ratio 4:3
As can be seen digital sensors, regardless of the number of pixels they support have a 4:3 aspect ratio.
So what happens when we try to fit a digital photo on a 4X6 paper? The photo just doesnt fit! it is either too wide or too high. For example if we want to print on the full 4 inches height we will only fill 51/3 inches (4X51/3 is a 4:3 aspect ratio) and 2/3 inches will be left blank.
To solve this problem and use the full paper size many printing services allow the user to crop a part of the photo. The assumption is that instead of leaving a blank area on the print the user would prefer to cut a part of the photo that is not important and use the whole paper for the rest. Some services allow the users to choose a preference for either cropping the photo or leaving a blank area on the print and this preference is automatically applied to all his prints.
What is a 4XD paper?
In light of the popularity of digital cameras and digital prints many printing services are introducing paper sizes that are designed for digital prints. This means that the aspect ratio of the paper they offer is 4:3 and thus photos taken with digital cameras perfectly fit the paper.
The new digital compatible paper sizes have an aspect ratio of 4:3 (the digital sensor aspect ratio) and are as close as possible to their traditional film paper sizes. So in the digital world a 4X6 paper size will actually become a 4X5 1/3 (a 4:3 aspect ratio paper size that is as close as possible to a 4X6 size).
As a marketing gimmick and instead of writing exact paper sizes many use the digital abbreviation of 4XD which means 4XDigital or in other words as close as we could make it to 4X6 that is digital camera aspect ratio compatible.

As digital cameras become more and more popular it is expected that more papers sizes which are digital camera compatible will be introduced. In a few years from now most printing services will support the digital paper size by default and the film compatible one will be the exception.